| California |
|---|
Synthetic control: weighted average of other units
Estimation…
\begin{align*} &\text{Synthetic California}_{t} = \\ &\quad w_{\text{Nevada}} \cdot \small{\text{Sales}}_{\text{Nevada}} + \\ &\quad w_{\text{Connecticut}} \cdot \small{\text{Sales}}_{\text{Connecticut}} + \\ &\quad w_{\text{Colorado}} \cdot \small{\text{Sales}}_{\text{Colorado}} + \\ &\quad w_{\text{Montana}} \cdot \small{\text{Sales}}_{\text{Montana}} + \\ &\quad w_{\text{Utah}} \cdot \small{\text{Sales}}_{\text{Utah}} \end{align*}
| California |
|---|
| 0.17 |
| 24.28 |
| 10.12 |
| Predictor | Colorado | Connecticut | Montana | Nevada | Utah |
|---|---|---|---|---|---|
| age15to24 | 0.16 | 0.16 | 0.15 | 0.15 | 0.18 |
| beer | 25.08 | 20.70 | 27.88 | 37.00 | 13.34 |
| lnincome | 10.00 | 10.27 | 9.76 | 10.05 | 9.71 |
| California |
|---|
| 0.17 |
| 24.28 |
| 10.12 |
=
| Predictor | Colorado | Connecticut | Montana | Nevada | Utah |
|---|---|---|---|---|---|
| age15to24 | W_Col*0.16 | W_Con*0.16 | W_Mon*0.15 | W_Nev*0.15 | W_Utah*0.18 |
| beer | W_Col*25.08 | W_Con*20.7 | W_Mon*27.88 | W_Nev*37 | W_Utah*13.34 |
| lnincome | W_Col*10 | W_Con*10.27 | W_Mon*9.76 | W_Nev*10.05 | W_Utah*9.71 |
The synthetic control was developed by Alberto Abadie and collaborators.
It’s pretty easy with the tidysynth package.
Bayesian synthetic control for goals 1 & 2
So far, goal 1:
Data generated with a multiple regression linear model unobserved and observed (normal) predictors
Additive causal effect (+400 at all time points)
| Simulation results | ||||
| Method | Standard Deviation | Bias | MSE | Coverage |
|---|---|---|---|---|
| Maximum a Posteriori | 47 | 0.98 | 2,252 | - |
| Posterior mean | 92 | 3.73 | 8,472 | 0.24 |
| Current implementation | 45 | 1.81 | 2,001 | - |
Modelling:
More simulation conditions, including time-varying coefficients
Goal 2: Multiple treated units
Thanks to my supervisors Oisín Ryan & Erik-Jan van Kesteren
Thanks for listening!